Golf Club Head and Method of Varying Moment of Inertia of Same

ABSTRACT

Methods of optimizing mass characteristics of golf club heads, particularly moment of inertia and the position of center of gravity, and a golf club head with an optimized moment of inertia are disclosed. In one embodiment of the invention, the moment of inertia of the club head is controlled by allocating the mass of the club head relative to the location of a centroid radius of the sole. In another embodiment of the present invention, a sole is modeled on two-dimensional matrices to determine the change in moment of inertia due to shifts in mass concentration around the sole. In another embodiment of the present invention, a sole is modeled on two-dimensional matrices to determine the shift in position of the center of gravity of the sole due to shifts in mass concentration around the sole.

FIELD OF THE INVENTION

The present invention relates to golf club heads, and more specifically, to optimizing the moment of inertia of driver golf club heads and a method for manipulating the mass characteristics of golf club heads.

BACKGROUND OF THE INVENTION

Manipulation of mass distribution in golf club heads can improve club head characteristics such as center of gravity and moment of inertia. Driver club heads typically consist of a crown, a sole, a skirt disposed in between the crown and sole and a hitting face. Changes in the distribution of weight between these portions of the club head vary the center of gravity or moment of inertia of the club head, and thus produce changes in the characteristics of the impact between the club head and a golf ball and the flight path of the golf ball.

Golfers of all skill levels may benefit from using golf clubs having high moments of inertia, as the moment of inertia of a golf club head influences the degree to which an off-center hit will send a golf ball off of its intended trajectory. Hooks and slices are produced when a golf club head makes contact with a golf ball at a location off to the side of the center of gravity of the club head, imparting side-spin to the golf ball and causing it to veer off of its intended path. Golfers who have difficulty connecting the golf club head with the golf ball at the sweet spot would benefit from using a golf club head that has a high moment of inertia. The greater the moment of inertia of the club head, the more resistant the club head will be to undesired rotational movement about the axis that runs vertically through the center of gravity of the golf club head, referred to hereinafter as the z-axis. The less the club head moves about the z-axis as it makes contact with the golf ball, the less side-spin it will impart to the golf ball. This would, in turn, mitigate the severity of the hook or slice.

Golfers who are able to exercise great control over the location of the impact between the club head and the golf ball often use this skill to their advantage by intentionally imparting spin to the golf ball. These skilled players can achieve added control over the movement of the golf ball by using golf clubs with improved moments of inertia.

A number of methods have been developed to produce golf club heads with mass distributions that improve mass characteristics of the club heads. One method, disclosed in U.S. Pat. No. 6,386,990, is to include pieces of weighted material in the body of the club head. The '990 patent discloses a golf club head consisting of a face, a sole, a crown and a skirt disposed in between the crown and sole made of a composite material. A strip of material having a greater density than the composite material is disposed to the skirt of the club head. In another example, U.S. Pat. No. 7,147,573 discloses a golf club head with a recess extending through the body of the club head in an arc-like shape from the heel end to the toe end. Within this recess is a cable, attached to which is at least one weight member that may be moved to vary the mass characteristics of the club head.

Another method of manipulating mass characteristics is to construct a golf club head having components of different materials. For example, U.S. Pat. No. 7,144,336 discloses a golf club head composed of a periphery member, comprising a sole wall, a toe wall, a hosel and a heel wall; a central member, comprising a body with forward, rear, sole, top, toe and heel surfaces; and a face plate. The periphery member is made of a high density metal material such as nickel-tungsten alloy, the central member is composed of a lightweight, non-metal material, and the face plate is composed of a lightweight metal material such as titanium alloy.

Another attempt to manipulate mass characteristics involves changing the shape of the golf club head. For instance, U.S. Pat. No. 7,077,758 discloses a putter having an arrangement of components wherein the majority of the mass is situated within three or more separate positions that are approximately equidistant from the center of mass of the club head. These three positions lie inside a “mass ring”, the outside diameter of which is approximately the same length as the distance between the ends of the putter striking face.

These examples of the prior art describe ways to vary the mass characteristics of golf club heads, however they do not disclose a method applicable to a broad range of styles of golf club heads for optimizing mass characteristics, specifically moment of inertia. Hence, a need exists in the art for a golf club head having an optimized moment of inertia. There is also a need for a method of determining how to optimize the mass characteristics of a golf club head.

SUMMARY OF THE INVENTION

The present invention is directed to a golf club head with an optimized moment of inertia (MOI).

The present invention is also directed to a method of controlling mass characteristics of golf club heads.

The present invention is preferably directed to a golf club head having a crown, face, skirt and sole, such that the distribution of mass in the sole affects the moment of inertia of the club head. In one embodiment of the present invention, the mass of the sole is allocated relative to the location of a centroid radius of the sole. When more of the sole's mass is allocated outside of the centroid radius of the sole, the moment of inertia of the sole is increased. By extension, the moment of inertia of the entire club head, when all other mass characteristics of the crown, face, and skirt remain constant, is increased.

A method for determining the centroid radius is also disclosed. In accordance with this aspect of the present invention, the centroid radius is defined as the distance located on the sole and radially away from a reference point on the sole through which an axis of rotation runs, at which the moment of inertia (MOI) of the sole would change from a reduction relative to a designated baseline MOI to an increase relative to the designated baseline MOI when more of the sole's mass is located beyond that centroid radius. The reference point can also coincide with the hosel, a center of gravity of the club head or a center of gravity of the club head.

In another embodiment of the present invention, a method of optimizing the MOI of a golf club head sole is presented. Mass is distributed in an arc-like pattern on the sole, said arcs radiating away from a reference location that coincides with the axis of rotation of the club head, said axis can be as the shaft of the club, to determine the location on the sole where mass reallocation results in greater MOI than a baseline MOI calculated in regard to a sole having uniform density, thickness and mass distribution.

Yet another embodiment of the present invention discloses a method of optimizing mass distribution to balance the center of gravity of the club head and MOI. Due to the concavity of the sole, center of gravity will shift upward and rearward as more mass is moved radially outward to increase MOI. A balance between these factors can be obtained to maximize mass properties or to individually customize clubs.

In other embodiments of the present invention, a golf club head is presented having a sole composed of areas of various materials, said areas being located relative to a centroid radius in order to optimize MOI of the club head.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a bottom perspective view of a golf club head having a sole with areas of varying mass distribution according to the present invention;

FIG. 2 is a back view of the golf club head of FIG. 1 according to the present invention;

FIG. 3 is a top perspective view of the golf club head of FIG. 1 according to the present invention;

FIG. 4 is a matrix showing a two-dimensional baseline model of a sole, each cell representing a point-mass of the sole;

FIG. 5 is a matrix showing a two-dimensional model of a sole, each cell showing an r² value—the square of the linear distance from that point mass to the point through which an axis of rotation runs;

FIG. 6 is a matrix showing a two-dimensional baseline model of a sole, each cell showing the moment of inertia of that point-mass on the sole relative to the z-axis running through the reference center of gravity of the club head;

FIG. 7 is a matrix showing a two-dimensional model of a sole having an arc-like region where a pre-determined amount of mass is allocated;

FIG. 8 is a matrix showing a two-dimensional model of a sole having an arc-like region that is greater in radial distance than the arc-like region of FIG. 7, in which a pre-determined amount of mass is allocated;

FIG. 9 is a top perspective view of an inventive golf club head with the crown cut-away;

FIG. 10 is a bottom perspective view of the golf club head of FIG. 9;

FIG. 11 is a right side view of the golf club head of FIG. 9;

FIG. 12 is a top view of a golf club head with the crown removed, showing the sole and its pattern of mass distribution;

FIG. 13 is a top plan view of a golf club head showing a crown that has areas of varying mass;

FIG. 14 is a bottom plan view of the golf club head of FIG. 14 showing a sole that has areas of varying mass;

FIG. 15 is a matrix showing a two-dimensional model of an inventive sole showing another mass distribution;

FIG. 16 is a matrix showing a two-dimensional model of a sole wherein each cell shows a number equal to the product of the mass of that cell, the x-coordinate of that cell, and a scale factor;

FIG. 17 is a matrix showing a two-dimensional model of a sole wherein each cell shows a number equal to the product of the mass of that cell, the y-coordinate of that cell, and a scale factor;

FIG. 18 is the mass matrix of FIG. 15 with the center of gravity in the x and y-directions highlighted;

FIG. 19 is a matrix showing another two-dimensional model of a sole wherein each cell is assigned a mass and wherein an arc-like area having a concentration of mass about a reference axis is highlighted;

FIGS. 20 and 21 are matrices similar to FIG. 19 with different arc-like areas having a concentration of mass highlighted;

FIG. 22 is a matrix showing a two-dimensional model of a concave sole wherein each cell is assigned a value corresponding to the vertical distance of that cell from the ground plane;

FIG. 23 is a chart on which center of gravity in the vertical, or z-direction, and moment of inertia are plotted against the average r value of the arc-like region of a sole in which mass is concentrated; and

FIG. 24 shows the matrix of FIG. 5 and also includes drawings to illustrate the method used to find the r² value of each element of the matrix.

DETAILED DESCRIPTION OF THE INVENTION

It is generally known that varying the distribution of mass in a golf club head will vary the MOI value of the golf club head. More specifically, by redistributing the mass of the club head away from a vertical reference axis, such as a vertical line going through the center of gravity, a geometric center or the hosel of the club head, the moment of inertia becomes larger than a baseline value of MOI measured on a club head with mass distributed evenly throughout the sole of the club head, hereinafter referred to as the baseline MOI. It is also generally known that if one were to concentrate mass in an area of the club head radially away from the center of gravity, the moment of inertia can increase. These changes in MOI affect the way the golf ball travels on mishits. The higher the MOI, the more forgiving on mishits or off-center hits.

What remains undisclosed in the art is the radial distance from the point on the sole directly beneath the center of gravity of the club head at which the moment of inertia would change from a reduction relative to the baseline MOI to an increase relative to the baseline MOI when more of the golf club head's mass is located beyond that radial distance. In accordance to one aspect of the present invention, that distance, hereinafter referred to as the centroid radius, is provided. In accordance to another aspect of the present invention, a method for finding the centroid radius is also provided. A similar centroid radius has been determined for golf balls in commonly-owned U.S. Pat. No. 6,494,795. The '795 patent is incorporated herein by reference in its entirety.

In a first embodiment of the present invention, the centroid radius of a driver club head is determined. In one example, a driver club head having a volume of 460 cm³ is used. Such a club head 10, shown in FIGS. 1-3, has a hitting face 12, crown 14, sole 16, toe 18 and heel 20. Club head 10 also has skirt 22, which connects crown 14 to sole 16, and hosel 24 adapted to receive a shaft (not shown).

Hitting face 12 should have a certain thickness to withstand repeated impacts with golf balls or a given thickness profile to maximize the energy transfer to the balls; accordingly, a limited amount of mass may be redistributed from the hitting face to improve MOI. Crown 14 and skirt 22 are generally already made sufficiently thin so that more mass can be relocated to the location(s) below the center of gravity. Hence, it is preferred in this embodiment that mass is not redistributed therefrom to improve MOI. In this embodiment, mass from sole 16 is redistributed therewithin to improve the MOI and a centroid radius is determined for club head 10 when the mass of sole 16 is redistributed. In other embodiments, discussed below, mass from other parts of the club head, namely the crown and skirt, is redistributed to regions on the sole to increase MOI.

The centroid radius can be found by modeling the sole of the golf club head on a two-dimensional graph or matrix and dividing the sole into equal square elements. Each element is considered a point-mass and is assigned a pair of coordinates to correspond with its location on the graph and also its location within the sole of the golf club head. In an example of such a matrix, as shown in FIG. 4, each square represents an area of 4.5 mm×4.5 mm on the sole; the vertical and horizontal coordinates shown on the top and left sides are divisible by 0.5 to show that the assigned coordinates relate to the center of the elements. Each element is also assigned a number value that corresponds to the mass of that element of the sole. In FIG. 4, the mass of the sole is evenly divided among the total cells in the two-dimensional model of the sole. The mass distribution illustrated in FIG. 4 represents the baseline MOI, discussed above. A similar two-dimensional model of the sole is created, although on this matrix each element is assigned an r² value—a number that corresponds to the square of the linear distance from that element to the selected reference point through the axis of rotation runs. An example of this matrix is shown in FIG. 5. The r² values assigned to the elements on this matrix are found using the Pythagorean Theorem and the point on the sole through which the axis of rotation runs is the shadow of the center of gravity of the club head onto the sole. FIG. 24 illustrates the method used to find the r² values of each element of the matrix. The dashed line indicates the axis of rotation, which runs vertically through the shaded element. It should be noted that any reference axis can be selected, and as discussed in more detail in other embodiments, a vertical axis going through the hosel is later selected as a reference axis.

Another two-dimensional model is made that is similar to the matrices of FIGS. 4 and 5, although on this model, an example of which can be seen in FIG. 6, each point reflects the value of moment of inertia of that point-mass of the sole, found by applying the formula presented in the Parallel Axis Theorem, where pm stands for “point-mass” and cm stands for “center of mass”:

I _(pm) =I _(cm) +mr ²

As each point mass has its own center of gravity, as well as contributes to creating a center of gravity of the sole, each point-mass has its own moment of inertia relative to an axis of rotation running through its center of mass. For the purposes of this embodiment, however, I_(cm) is omitted, as each point-mass is in and of itself a center of mass, causing I_(cm) to be negligibly small. To find the baseline MOI for the entire sole, the following formula is applied:

I _(sole) =ΣI _(pm) =Σmr ²

The centroid radius is determined by selecting a portion of the mass of the sole to be removed from the entire sole and re-distributed in an area of the sole that forms an arc-like or circular shape about the center of gravity, as shown in FIG. 7. Preferably, this arc shape substantially resembles the overall shape of the club head. As the shape of the sole, total mass of the sole and the arrangement of point-masses remain the same as in the baseline calculation, new moments of inertia for each point-mass can again be found using the formula:

I _(pm) =I _(cm) +mr ²

The sum of the individual moment of inertia values for this new pattern of mass distribution is found, as in the baseline model, to find the moment of inertia of the entire sole. The centroid radius can be determined by reallocating the pre-determined amount of mass to an arc-like area on the sole first immediately around the center of gravity and finding the resulting moment of inertia, and then reallocating the mass in arcs that radiate outward on the sole from the center of gravity in incremental steps and comparing the resulting values of moment of inertia to the baseline MOI. The centroid radius exists at the location where the moment of inertia value changes from less than the baseline value to greater than the baseline value.

With the knowledge of the location of the centroid radius, the moment of inertia of the golf club head sole can be increased or decreased relative to the baseline MOI by reallocating more of the sole's mass in the area outside or inside of the centroid radius. By extension, a golf club head can be made to have a greater or smaller moment of inertia as compared to a baseline club head in which the mass of the sole is evenly distributed by keeping the design of the crown, skirt, and face constant but reallocating most of the mass of the sole outside or inside of the centroid radius.

In an example of the first embodiment of present invention to illustrate the above-described method, the area of sole 16 is estimated to be about 2155.5 mm². The mass of sole 16 is set at about 50.0 grams. The mass of sole 16 to be re-distributed within the arc-like shape around the center of gravity is about 7.5 grams. The initial selected mean radial distance of the arc-like shape from the point on the sole directly below the center of gravity is about 12.57 mm. In accordance with an embodiment of the present invention, mean radial distance refers to the sum of the linear distances of all the elements that make up a designated arc-shaped area to the point on the sole directly below the center of gravity of the club head, divided by the total number of elements that make up the arc-shaped area. The arc-shaped area is then moved away from the center of gravity in a radial and incremental fashion. Though the center of gravity may shift in response to the redistribution of mass around the sole, in this example the centroid radius was determined with respect to the location of the center of gravity for a sole with an even distribution of mass, designated herein as the baseline sole model. Table 1 shows the results of the calculations.

TABLE 1 7.5 gram Mass Baseline Change in Mean r MOI New MOI MOI (mm) (g * cm{circumflex over ( )}2) (g * cm{circumflex over ( )}2) (g * cm{circumflex over ( )}2) 12.57 9357.6953 8336.0562 −1021.6391 17.50 9357.6953 8473.5518 −884.1435 22.44 9357.6953 8628.1495 −729.5458 27.35 9357.6953 8795.9576 −561.7377 32.07 9357.6953 8966.1029 −391.5924 36.45 9357.6953 9124.2331 −233.4622 41.08 9357.6953 9298.5965 −59.0988 45.40 9357.6953 9459.1811 101.4858 49.66 9357.6953 9617.3441 259.6488 54.10 9357.6953 9768.5221 410.8268 58.31 9357.6953 9911.4235 553.7282 62.48 9357.6953 10044.1567 686.4614

The results show that for a sole having an area of 2155.5 mm² and a mass of 50.0 grams, the centroid radius is located between arc-shaped areas about the center of gravity having mean radii of 41.08 and 45.40 mm. To produce a golf club sole with these measurements having a moment of inertia that is greater than that of a club sole with an evenly distributed mass, a pre-selected mass of the club head sole should be distributed in the area outside of the arc-shaped area located between 41.08 and 45.40 mm. This same method was used to compare moments of inertia for a club head sole with identical area and overall mass values as described above, but with arc-shaped areas in which 5.0 grams of mass were redistributed. As in the previous example, the centroid radius was determined in regard to the location of the center of gravity in a sole with an even distribution of mass The centroid radius for this mass-distribution was also located between 41.08 and 45.40 mm from the center of gravity. The results of these calculations are shown on Table 2.

TABLE 2 5.0 gram Mass Baseline Change in Mean r MOI New MOI MOI (mm) (g * cm{circumflex over ( )}2) (g * cm{circumflex over ( )}2) (g * cm{circumflex over ( )}2) 12.57 9357.6953 8766.4530 −591.2423 17.50 9357.6953 8866.7760 −490.9193 22.44 9357.6953 8971.7581 −385.9372 27.35 9357.6953 9077.1168 −280.5785 32.07 9357.6953 9175.2166 −182.4787 36.45 9357.6953 9254.7245 −102.9708 41.08 9357.6953 9334.1168 −23.5785 45.40 9357.6953 9394.9594 37.2641 49.66 9357.6953 9443.8838 86.1885 54.10 9357.6953 9469.0002 111.3049 58.31 9357.6953 9501.3721 143.6768 62.48 9357.6953 9551.2504 193.5551

After interpolation the centroid radius of the sole described in Table 1 had a mean radial distance of 42.67 mm. The centroid radius of the sole described in Table 2 had a mean radial distance of 42.75 mm. In accordance with the present invention, this method can be applied to club heads of all types, as any two-dimensional shape of the sole can be approximated on the graphs. The radial distance between arc-shaped areas of re-allocated mass can be decreased and the resolution of the graphs can be increased by using a greater number of cells to approximate the shape of the sole.

Preferably, this method of determining the centroid radius would be used to optimize moment of inertia for golf club heads. More preferably, the method would be used to optimize moment of inertia in driver-style golf club heads. Most preferably, the method would be used to optimize moment of inertia in driver-style or utility club heads having reached the limits proscribed by the United States Golf Association (USGA) for length, depth, height, and volume.

It should be noted that as different mass distributions are modeled using the methods described above, the center of gravity may move in response to the shifting mass pattern. In accordance with another embodiment of the present invention, the movement of the center of gravity around sole in response to changing mass patterns is determined. Specifically, this embodiment provides a method of determining center of gravity in the x and y directions that define the two-dimensional x-y plane used to model the sole of a golf club head in the previous embodiment. To calculate the location of the center of gravity in the x-direction, first the mass of each element of the sole model (as seen in FIG. 7) is multiplied by the x-coordinate value of that element. Then, the sum of the resulting values is found and divided by the value of the total mass. The resulting number provides the location in the x-direction of the center of gravity of the sole having its particular mass distribution pattern. To find the location of the center of gravity in the y-direction, first the mass of each element of the sole is multiplied by the y-coordinate value of that element. The sum of the resulting values is found and again divided by the value of the total mass. The resulting number provides the location in the y-direction of the center of gravity. To determine the movement of the center of gravity in response to changing mass distribution around the sole, the method described above should be repeated for each new pattern of mass distribution modeled.

The method described above is illustrated in FIGS. 15-18. FIG. 15 shows a matrix on which a sole is modeled, the sole being divided into individual elements. The mass distribution pattern is different than the one shown in FIGS. 7-8. In addition to having an arc of higher mass elements disposed radially away from the reference center of gravity, a central area comprising multiple lower mass elements is located proximate to the reference center of gravity. This pattern specifically removes mass from the center area where its contribution to the MOI is minimal and mass to the periphery where its contribution to MOI is maximized. Each element is assigned a mass, the sum of the masses of each element totaling 50 grams. FIG. 16 shows the same sole as modeled on a matrix, although each cell of this matrix shows a number which refers to the product of the mass of that element (from FIG. 15) and the coordinate position of that element on the x-axis. In the bottom right of the matrix, the center of gravity in the x-direction (in terms of the x-coordinate) is provided, this number being the result of the sum of numbers of all of the elements divided by the total mass of the sole. In this specific example, the numbers in the elements of the matrix of FIGS. 16 and 17 are the product of the mass of the element, the coordinate position (either x or y) and a scale factor of 4.5, as each coordinate should be multiplied by 4.5 to show the position in millimeters of the individual elements on the sole of this example (each cell of the matrix represents an area of 4.5 mm×4.5 mm). In FIG. 17 the elements of the sole model show the number resulting from the product of the mass of each element, the y-coordinate of each element and the scale factor of 4.5. Again, in the bottom right of the matrix, the center of gravity in the y-direction (in terms of the y-coordinate) is provided, this number being the result of the sum of numbers of all of the elements divided by the total mass of the sole. FIG. 18 shows the sole matrix, each element having an assigned mass as shown in FIG. 15, wherein the element that most closely coincides with the center of gravity coordinates—in this case being (10.70, 15.70)—is highlighted.

Table 3 shows the movement aftward of the center of gravity of the sole in the x-y plane for a model sole having an area of about 2155.5 mm², a total mass of about 50 grams and an arc-shaped region of mass concentration of about 7.5 grams. The rearward movement of the center of gravity of the sole is given in millimeters, while the position of the center of gravity is shown using x and y coordinates. The position of the center of gravity of the club head would be affected by the mass distribution of the sole, however the movement of the center of gravity of the club head would be substantially less than the movement of the center of gravity of the sole, owing to the contribution of the mass of the crown, skirt, face and hosel to the center of gravity of the club head.

TABLE 3 7.5 gram Mass Rearward Mean r Baseline CG Movement of CG (mm) CG (x, y) (x, y) (mm) of sole 10.82 (10.19, 15.50) (6.50, 15.50) 16.62 mm 13.55 (10.28, 15.49) (6.50, 15.50) 17.02 mm 16.93 (10.37, 15.49) (6.50, 15.50) 17.39 mm 52.90 (10.72, 15.50) (6.50, 15.50) 18.97 mm

In a third embodiment of the present invention, a second centroid radius is determined, this centroid radius being calculated with respect to an axis of rotation that corresponds to the shaft of the club. As in the first embodiment shown in FIGS. 5-8, a matrix is developed to model a sole of a golf club in two dimensions. The sole model is divided into equally-sized elements, each element having a coordinate position to show the location of that element with respect to the entire sole. In a first matrix, each element is assigned a mass. In a second matrix, the r² value is determined for each element, said r² value being the square of the distance of that element from the designated location of the axis of rotation, said axis having a location that coincides with the shaft of the club. In a third matrix, each element shows a MOI value-the result of the product of the mass of that element and the r² value of that element. The moments of inertia of each element are added to find the MOI of the entire sole. To determine the centroid radius, the MOI values of various patterns of mass distribution are compared to a baseline MOI, said baseline MOI being calculated with respect to a sole having a uniform density, thickness and mass distribution.

As illustrated in FIGS. 19-21 by the pattern of highlighted elements, MOI should be determined for the sole wherein a portion of the entire mass of the sole is reallocated to an arc-like area surrounding the location on the sole where the shaft meets the sole, otherwise known as the hosel location. Subsequent calculations of MOI should be performed for the sole, wherein the portion of mass is allocated to arc-like areas radiating away from the location of the axis of rotation. To determine the location of the centroid radius, the MOI values for each pattern of mass allocation are compared to the baseline MOI to find a mass distribution that results in a MOI greater than that of the baseline MOI. For each arc-like area, a mean radial distance (mean r) is determined, said mean r value being the average of the distance r of each element in the arc-like area from the axis of rotation.

In an example of the third embodiment, the centroid radius with respect to a vertical or z-axis of rotation having a location that coincides with the shaft of the club was determined for a sole having a mass of 50 grams and an area of about 2155.5 mm². The baseline MOI of inertia for said sole was calculated using the method described above. Then, a 7.5 gram mass was removed from the entire sole and reallocated to an arc-like area on the sole having a mean radial distance (mean r) of 12.07 mm. Moment of inertia of the sole was then calculated. Eleven subsequent mass distributions were performed, the arc-like areas increasing in r value from 26.06 mm to 105.39 mm. Moments of inertia were calculated for each new mass distribution and compared to the baseline. According to this example of the third embodiment, the centroid radius for a sole having a mass of 50 grams and an area of about 2155.5 mm² , wherein 7.5 grams of the 50 gram mass are allocated to an arc-like area located radially away from the hosel location on the sole, is located between arc-like areas having r values of 67.89 mm and 76.19 mm. More specifically, the centroid radius relative to a vertical axis through the hosel is interpolated to be about 69.6 mm. Table 4 shows the results of the above-described example.

TABLE 4 7.5 gram Mass Baseline Change in Mean r MOI New MOI MOI (mm) (g * cm{circumflex over ( )}2) (g * cm{circumflex over ( )}2) (g * cm{circumflex over ( )}2) 12.07 24299.5694 21139.2883 −3160.2811 26.06 24299.5694 21586.5148 −2713.0546 35.29 24299.5694 22052.9771 −2246.5923 45.46 24299.5694 22642.8924 −1656.6770 55.82 24299.5694 23333.3988 −966.1706 61.44 24299.5694 23711.2555 −588.3139 67.89 24299.5694 24168.5198 −131.0496 76.19 24299.5694 24807.5277 507.9583 84.81 24299.5694 25506.6172 1207.0478 90.74 24299.5694 26043.6637 1744.0943 97.23 24299.5694 26674.7456 2375.1762 105.39 24299.5694 27469.7779 3170.2085

In a fourth embodiment of the present invention, a method of tracking shifts in MOI and center of gravity in the vertical direction due to mass distribution in a sole of a golf club head is used to optimize both MOI and the position of center of gravity of a club head. Starting in the center of the sole and radiating toward the heel, toe, back and face, a typical sole curves up and away from the ground plane. Concentrating mass in the perimeter areas of the sole, or outside of the centroid radius as defined in previous embodiments, will generally result in an increase of MOI as compared to a baseline MOI; however, that concentration of mass may also cause the center of gravity of the club head to move up, toward the crown, as more mass is located in areas of the sole that are farther away from the ground plane.

To increase MOI but keep the center of gravity of the club head acceptably low, a first two-dimensional matrix is created to model the sole. The sole is divided into equally-sized elements, each element corresponding to a set of coordinates to show the position of that element in the sole. Each element is also labeled with a number representing the r value of that particular element. In this embodiment, r refers to the distance of the element from the location on the sole on which the club head's center of gravity is projected and through which an axis of rotation runs.

A second matrix is created to model the same sole; however, the elements of this matrix are labeled with a z-value, z referring to the vertical distance of the element to the ground plane. This second matrix takes into account the curved nature of the sole of the golf club. FIG. 22 shows an example of a matrix created in accordance with this aspect of the invention. A third matrix is created to show the mass of each element in a particular mass pattern. Like the method described above to find the center of gravity of the sole in the x and y directions, the center of gravity of the sole in the vertical z-direction can be found by multiplying each element in the second matrix by its corresponding element in the third matrix, finding the sum of all of the resulting numbers, and dividing that sum by the total mass of the sole.

For each new pattern of mass distribution, which can be manipulated by assigning mass values to the elements of the third matrix, the center of gravity in the z direction should be calculated. The shift in vertical position of the center of gravity due to mass distribution in the sole can be charted against the mean radial distance (mean r) of the area in which mass was concentrated (for instance, an arc-like area surrounding the axis of rotation) to provide a visual representation of the change in position. To track the change in MOI of the sole, for each pattern of mass distribution for which a center of gravity in the z-direction was found, the elements of the third matrix are multiplied by the square of the value of the corresponding elements of the first matrix, and the resulting numbers are added together. This sum is the total MOI of the sole.

The shift in MOI can be charted on the same graph used to show the shift in center of gravity in the z direction, the resulting graph offering a visual representation of the movement of the center of gravity and the changing value of MOI due to shifts in mass concentration around the sole. An example of such a graph is shown in FIG. 23, wherein the shift in vertical position of the center of gravity of the sole and the change in MOI are plotted against the mean radial distance (mean r)—r the average distance of the elements that make up the arc-like area of mass from the location of the center of gravity on the sole—of the arc-like area of mass in which mass was allocated for a particular sole. As is shown in FIG. 23, the graph can be a tool to club designers, allowing them to see how a particular mass distribution pattern will improve the playability of a club, and offering a clear view of how substantial increases in MOI may be achieved while preventing center of gravity from shifting too far toward the crown. Center of gravity in the x-y plane, as described above, can be added to this graph to optimize the aft-position of center of gravity. Alternatively, after MOI and center of gravity have been calculated for various patterns of mass distribution, the matrices may be consulted and/or labeled to show areas where mass may be allocated or removed in order to achieve optimized MOI and center of gravity position.

It is possible to determine the centroid radius of the sole of a golf club through other methods, as well. In accordance with another embodiment, the centroid radius can be found using classical mathematics equations for the moments of inertia of objects with varying shapes. The centroid radius can be determined this way by following these steps:

-   -   1) Determine the baseline MOI of sole 16 (or club head 10).         -   a) Divide club head or sole into well-defined geometrical             regions, e.g., circular arcs, circular segments, polygons,             etc.         -   b) Determine the mass of each region.         -   c) Determine the mean distance of each region to the center             of gravity of the club head or to the location on the sole             that represents the center of gravity of the club head.         -   d) Using known inertia equations, including the equation             presented in the Parallel Axis Theorem, for each geometrical             region relative to the y-axis through the center of gravity,             find the inertia of each region. Such inertia equations are             available in texts such as CRC Standard Mathematical Tables,             24^(th) Edition, 1976 and The Cambridge Handbook of Physics             Formulas, 2000.

Parallel Axis Theorem: I _(region) =I _(cm) +mr ²

-   -   -   e) Sum the inertia values for all the geometrical shapes to             determine the MOI of the club head or sole using the formula             offered by the Parallel Axis Theorem:

I_(sole)=ΣI_(region)

-   -   2) Determine the MOI of sole 16 or club head 10 with radiating         arc-like area(s) of reallocated mass.     -   a) Determine the amount of mass available for redistribution.         -   b) Distribute the mass of step 2a in arc-like areas on the             sole and/or on the crown and/or the skirt.         -   c) Repeat steps 1a to 1e to determine the MOI for each sole             or club head with a new pattern of mass distribution.         -   d) Determine the centroid radius by comparing the MOIs in             step 2 with the baseline MOI in step 1.

Yet another method for determining centroid radius involves modeling the sole of the club using Computer Aided Design, hereinafter referred to as CAD. To find a baseline moment of inertia for a sole with an evenly distributed, pre-determined mass and a known area, one can draw the object using CAD and then find its moment of inertia about the axis of rotation of the club head using software such as Inventor by Autodesk or SketchCalc by Cadvantage. The centroid radius can be found by drawing arc-like shapes or ring segments that have a mass equal to the amount of mass to be removed from the sole and/or other elements of the club head and reallocated in an arc-shaped area about the axis of rotation of the club head. The new moment of inertia with a redistributed pattern of mass can be determined by finding the moment of inertia of the arc-like shape and adding that value to the moment of inertia of the sole having a mass equal to the mass of the baseline sole model minus the amount of mass disposed into the arc-like shape. Repeating this process for arc-like shapes that have incrementally increasing radial distances from the axis of rotation of the club head, one can determine the radial distance at which the moment of inertia of the sole with a manipulated mass distribution will become greater than that of the baseline sole model when most of the sole's mass is distributed beyond that distance.

An example of CAD modeling is illustrated in FIGS. 9-1 1. In FIGS. 9 and 1, club head 110 shows center of gravity 134. Sole 116 of club head 110 contains portions 126, the area of the sole directly beneath center of gravity 134, and portion 128, the area surrounding 126. In accordance with an aspect of the invention, Portions 126 and 128 are located inside the centroid radius and are made of lightweight materials. More preferably, portions 126 and 128 are made of composite. FIG. 10 shows a bottom perspective view of club head 110 having portions 126 and 128 on sole 116. FIGS. 10 and 11 also show element 136 i, one of the many pieces of the CAD drawing having finite mass and area values that makes up part of the whole of club head 116. In accordance with another aspect of the present invention, the moment of inertia of club head 110 can be calculated using Finite Element Method (FEM), a technique that treats the whole geometry of the club head as a collection of piecewise linear functions, approximating a solution to what was formerly an integral equation. Finite Difference (FD) can also be used.

Referring again to FIGS. 1-3, in accordance to one aspect of the present invention, club head 10 is a high moment of inertia club head having a sole 16 that contains designated portions: a first portion 26 that lies directly below the center of gravity of the club head, a second portion 28 immediately surrounding the first portion and the remaining portion 30 of the sole 16. Portions 26 and 28 are made of lightweight materials and are located inside the centroid radius. Preferably, portions 26 and 28 are made of composite or other lightweight materials. Remaining portion 30 and at least part of skirt 22 are preferably composed of heavier materials and are located outside of the centroid radius. More preferably, remaining portion 30 and at least part of skirt 22 are composed of titanium, other metals or high density materials.

In accordance with another aspect of the present invention, FIG. 12 shows a golf club head, generally designated 210. Sole 216 of club head 210 contains a plurality of rings 230 a-230 e. Rings 230 a-e lie outside of the centroid radius and are preferably made of heavier materials. Most preferably, rings 230 a-e are made of titanium or other metals.

FIGS. 13 and 14 also show golf club head 210 having designated points 234 a and 234 b on the crown and sole respectively through which the y-axis runs, i.e. the points on the crown and sole that represent the location of the center of gravity of club head 210. Areas 232 a and b on crown 214 lie inside the centroid radius and are composed of lightweight materials. More preferably, areas 232 a and b are composed of composite. Likewise, areas 228 a and b and 226 on sole 216 lie inside the centroid radius are composed of lightweight materials. More preferably, areas 228 a and b and 226 are composed of composite.

Alternatively, the baseline MOI can be the MOI of any commercially available club heads that do not have constant thickness or do not have a sole with constant thickness. The baseline MOI can be calculated using any of the methods described above or it can be measured using an inertia instrument. For example, Model MOI-005-104 by Inertia Dynamics includes a plate affixed atop the body of the instrument to which a golf club head is secured via the hosel. The plate rotates the club head, measuring the period of one oscillation to determine the moment of inertia.

While various descriptions of the present invention have been explained herein, it is understood that the features of the present invention can be used singly or in combination with each other. Therefore, this invention is not to be limited to the specifically preferred embodiments depicted herein. 

1. A golf club head comprising a face, a crown, a skirt, and a sole, wherein the sole comprises at least a first weight located radially outside of a centroid radius of the sole, and wherein said first weight is denser or thicker than the rest of the sole so that the moment of inertia of the club head is higher than a baseline moment of inertia where the sole has a uniform mass, and wherein the centroid radius is calculated from a predetermined reference axis.
 2. The golf club head of claim 1, wherein the first weight has an arc-like shape that is similar to a rear contour of the club head, and the predetermined reference axis comprises a vertical axis extending through a center of gravity of the club head with the sole with uniform mass.
 3. The golf club head of claim 1, wherein at least a portion of the sole located inside the centroid radius is composed of lightweight materials.
 4. The golf club head of claim 1, wherein the weight of has an arc-like shape that is similar to the contour of the rear-toe region of the club head, and the predetermined reference axis is a vertical axis going through a hosel.
 5. The golf club head of claim 3, wherein said portion of the sole located inside the centroid radius is composed of titanium.
 6. A method for increasing the moment of inertia of a golf club head, comprising the steps of (a) determining a centroid radius for a sole of the golf club head; and (b) reallocating a portion of the mass of the golf club head to a location radially outside of the centroid radius.
 7. The method of claim 6, wherein in step (b), a portion of the sole is reallocated to said location.
 8. The method of claim 6, wherein step (a) comprises the steps of (i) selecting a reference axis; (ii) determining a baseline moment of inertia of the sole relative to said reference axis; (iii) reallocating a portion of the mass of the sole radially outward from a designated location on the sole through which an axis of rotation runs; (iv) determining a moment of inertia of the sole of step (iii); (v) repeating steps (iii)-(iv) for a predetermined number of iterations, wherein the radial distance of the reallocated portion of mass from the center of gravity changes with each iteration; and (vi) selecting the centroid radius at the radial location where the moment of inertia of step (iii) changes from being less than the baseline moment of inertia to being greater than the baseline moment of inertia.
 9. The method of claim 6, wherein the calculations are performed on two-dimensional matrices.
 10. A method of determining the center of gravity of a sole of a golf club head comprising the steps of (i) dividing the sole into portions of equal size; (ii) assigning each portion a value in the x, y and z directions corresponding to the position of each portion relative to the entire sole; (iii) assigning each portion a mass; (iv) finding the products of the mass of each portion and its corresponding x value, finding the sum of said products, and dividing the sum by the total mass of the sole to find the center of gravity in the x-direction; (v) repeating step (iv), substituting the x-value for the y-value to find the center of gravity in the y-direction; and (vi) repeating step (iv), substituting the x-value for the z-value to find the center of gravity in the z-direction.
 11. A method of optimizing the mass characteristics of a golf club head comprising the steps of (i) finding the moments of inertia of a sole according to the method of claim 8; (ii) finding the center of gravity in the vertical z-direction according to the method of claim 10 for each distribution of mass around the sole for which moment of inertia was calculated in step (i); and (iii) plotting the change in center of gravity in the vertical z-direction and the change in moment of inertia against the average value of distance from a designated axis of rotation of each portion of the sole that comprised the area in which mass was concentrated
 12. The golf club head of claim 3, wherein said portion of the sole located inside the centroid radius is composed of composite.
 13. The golf club head of claim 1, further comprising at least two weights located outside of the centroid radius of the sole.
 14. The golf club head of claim 1, further comprising at least three weights located outside of the centroid radius of the sole.
 15. The golf club head of claim 1, wherein said weight is composed of tungsten.
 16. A golf club head comprising a face, a crown and a sole, the sole comprising: at least two points, each point having an area of 4.5 mm by 4.5 mm and each point having a point-mass; at least a first zone having at least one point with a first point-mass; and at least a second zone having at least one point with a second point-mass, wherein the first point-mass is at least two times the second point-mass.
 17. The golf club head of claim 16 wherein the first zone has an arc-like shape that is similar to the contour of the rear-toe region of the club head.
 18. The golf club head of claim 16, wherein the first zone has an arc-like shape that is located radially outside of a centroid radius of the sole, wherein the centroid radius is calculated from a pre-determined reference axis.
 19. The golf club head of claim 16, wherein the first zone is a weight that is denser or thicker than the remainder of the sole.
 20. The golf club head of claim 16, wherein the first point-mass is at least 2.3 times the second point-mass. 